Is it a valid assumption that a purely MLP based tic-tac-toe player will learn lookahead strategies?
A MLP only does pattern recognition, it will not learn search. 

Tictactoe, (Oughts and Crosses), is such a simple game that your network should learn the moves from the training data by heart, no generalisation required. If it still loses games, maybe your training data doesn't consist of particularly good moves.